A mathematical model describing this anthropomorphism was developed in the 1960s in the United States by Aerospace Medical Research Laboratories in Dayton, Ohio. This model, well known as the Hanavan model, describes in a parametric manner, relative to given human size and weight, the dimensions of all the parts of the body. For example, the hip is described as a joint having three degrees of freedom in rotation. The dimensions of the hip and of the parts of the body surrounding it, pelvis and thigh, are also described. For example, for a 14-year-old adolescent 1.6 m tall and weighing 50 kg, the thigh can be represented by a truncated cone 392 mm high, with 46 mm for the small radius and with 74 mm for the large radius. For the same robot and using this model, the pelvis is represented by a parallelepiped 189 mm high, 230 mm wide and 160 mm deep. The distance between the two hips is equal to twice the large radius of the thigh. The height of the thigh is defined as the distance between the joint formed by the hip and that formed by the knee.
A dynamic calculation shows that, to achieve a gait at a speed of 1.2 m/s, and still for a robot of 1.6 m and 50 kg, the joint of the hip in the sagittal plane requires a torque of the order of 45 N·m, with a maximum speed of 2.7 rad/s, and an articular range of movement from −30° to +30°. Conversely, in the frontal plane, the joint requires a torque of the order of 35 N·m, with a maximum speed of the order of 1 rad/s and a motion range from −5° to +10°.
Currently, many humanoid robots have been developed, but not one complies with the Hanavan model, notably with respect to the size of the leg and the shoulder. For example, there are robots of which the hip is reduced to a universal joint type, that is to say comprising only two degrees of freedom, a rotation in the sagittal plane and a rotation in the frontal plane. Moreover, the actuation mechanisms used to motorize these two degrees of freedom, following the parameters originating from the dynamic calculation, depart from the dimensions specified in the Hanavan model. There are also robots in which the angular range of movement of the hip in the sagittal plane of the robot does not make it possible to obtain a sufficient step length to obtain a walking speed of the robot that is similar to that of a human.